B787 Captain reported flight deck oxygen for masks became completely depleted during cruise. Flight crew returned to departure airport for maintenance action.

Narrative

At the Gate:During ZZZ preflight; the flight deck oxygen was shut off for about 45 minutes. So; we called and were told this was due to O2 servicing as part of the ETOPS service check. What we did not know -- and could not see due to it being a maintenance-initiated action -- was that the inbound O2 pressure had been discovered to be zero following the flight from ZZZZ. That crew must not have gotten the EICAS; or it happened after they left the aircraft. Either way; maintenance elected to change an O2 bottle. Before we closed the door; I requested the maintenance tech come to the flight deck to ensure our masks were working correctly. He did so; and the oxygen level was checked to be 1700 psi. All four oxygen masks were tested; and all mask-door positions were checked before departure. They were left alone after that. The tech did not explain the extent of the maintenance performed or any issues encountered due to that maintenance.About 20 minutes later; we finally got the release and departed late. I reviewed the current release only and did not dig into the new maintenance history as I had no indication that anything other than servicing" had occurred. (See maintenance part of resolution narrative later in this report.)During cruise:About 5 hours into the flight to ZZZZ1; we got an EICAS; "CREW OXYGEN LOW." The checklist was very short and confirmed the situation. After completing the checklist; our O2 pressure indicated about 800 psi. But; when we checked our masks; the flight deck oxygen pressure went to zero; and all four masks went flat -- NO oxygen available! We immediately brought four walk-around 02 bottles to the flight deck to ensure a source of oxygen in the event of depressurization. We then called Maintenance Control and Dispatch and patched in the Chief Pilot. All agreed that we could NOT continue to ZZZZ1 because operation with just walk-around bottles did not meet safety standards in the event of fire and/or smoke. So; we decided our best option was to turn back to ZZZ1. The diversion and overweight checklists were both run. FOM X.XX.X was reviewed. With Maintenance Control and Dispatch input; and due to the high approach speeds for overweight and flaps 25 versus 30; we elected to jettison about 25;000 pounds of fuel at FL270 to facilitate landing at maximum landing weight.The diversion and landing just under MLW in ZZZ1 were both uneventful. Per the FOM diversion recovery guide; the crew stayed with the aircraft until passengers were deplaned; and the aircraft was turned over to ZZZ1 Maintenance.The value of communication was evident during this event. The divert itself was coordinated via a "urgent" message through CPDLC. This was interpreted as having [requested priority handling]; though we had not. The only emergency authority used was to dump the fuel."